Coulomb interaction and charge neutrality: Pariser, Parr and Pople Hamiltonian versus the Extended Hubbard Hamiltonian

TL;DR

This paper compares the Pariser-Parr-Pople Hamiltonian with the Extended Hubbard Hamiltonian, highlighting issues with charge inhomogeneities due to non-local interactions in finite systems, especially in 2D materials.

Contribution

It clarifies the relationship between two Hamiltonians used in quantum chemistry and condensed matter, emphasizing the impact of non-local interactions on charge neutrality.

Findings

Non-local interactions can cause unphysical charge inhomogeneities.

System size increase does not fully mitigate charge inhomogeneities for infinite-range potentials.

Dimensionality influences the severity of charge inhomogeneities in 2D systems.

Abstract

The Extended Hubbard Hamiltonian used by the Condensed Matter community is nothing but a simplified version of the Pariser, Parr and Pople Hamiltonian, well established in the Quantum Chemistry community as a powerful tool to describe the electronic structure of {\pi}-conjugated planar Polycyclic Aromatic Hydrocarbons (PAH). We show that whenever the interaction potential is non-local, unphysical charge inhomogeneities may show up in finite systems, provided that electrons are not neutralized by the ion charges. Increasing the system size does not solve the problem when the potential has an infinite range, and for finite range potentials these charge inhomogeneities become slowly less important as the potential range decreases and/or the system size increases. Dimensionality does also play a major role. Examples in bi-dimensional systems, such as planar PAH and graphene, are discussed to some extent.